“Constant Velocity” Conclusion

Lab reports for the buggy lab are due in a couple days, and I realized yesterday that I hadn’t really identified the central question of this lab… Oops! I tried to make up for this by calling explicit attention to it in class during our “peer review” of reports.

It’s tricky, because we haven’t defined velocity when we do the lab, so this isn’t precisely a “research question”, then we kind of use this one example to extrapolate to a number of different situations. The question itself is a fundamentally important one, but it’s mixed up in all the assumptions we make when we do our worksheet simplifications.

We’ll see how they do answering this question kind of after the fact. If they’ve been thinking carefully so far, it should be no problem!

##cvpm ##paradigmlab ##physicsfirst ##setbacks

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Stroboscopic Photos

I’ve introduced a “driving question” for the CVPM unit as, “How do we analyze motion?” thinking that it’s more exciting to frame CVPM as our most basic tool/approximation in a much larger toolkit than simply a description of things moving at a constant velocity.

Today we introduced motion maps briefly, by first showing off a few of these stroboscopic photos I found online. There are a number of awesome ones in LIFE magazine from the 40s that are particularly beautiful.

I made a little compilation here:
https://sites.google.com/site/packerphysics9/constant-velocity-particle-model/stroboscopic-photographs

One word of caution, if you search Google for “stroboscopic photography”, a number of the first hits that come up show nude women, strangely!

##cvpm ##representations ##physicsfirst

Buggy Uncertainty Insights

I’ve been making a big deal out of uncertainty this year, and I’m excited by what I’m seeing. During our first buggy lab whiteboarding, a student pointed out something fascinating about his group’s results. He noticed that there appeared to be a lot of variability between the points, but each SET of points collected during one trial seemed to fall in a nice straight line. This, he thought, meant that there was more variability in how the buggy was placed than how the salt packets were being placed.

Wow… So clever!!

(Check out the whiteboard peeker – my students have been doing this a lot lately when I snap board photos… Ha!!)

##cvpm ##ema ##uncertainty ##whiteboarding ##physicsfirst ##paradigmlab

Notes on Consensus and Extrapolating Ideas

I’ve been working hard this year to encourage students to document their understanding as they gain it, to use conscientious note-taking to create a resource for themselves as they go through the course. This means asking them repeatedly, “What could we write down about this that might be important for the future?” and getting some very blank stares.

It’s a task that’s very difficult for the students, and understandably so. Solving a specific problem correctly, or writing down a corrected solution that someone else has solved, involves much different thinking than extrapolating from that example what big ideas are actually at play. But I’m convinced that there’s a lot to gain by encouraging students to work on it time and time again.

Following a practice sheet on displacement, designed to encourage students to see how positive and negative signs can indicate the direction that the object has moved, I devoted 20 minutes of class time to discussing “big ideas” that could be recorded in the Consensus Notebook. At the end of that time (which consisted of both small group and whole class discussion), we’d come to consensus on one tiny thing – that displacement of an object is the same regardless of where on the object position was measured. Whew!!

For homework, I asked students to email to me a sentence or two describing something else that we might write in “CVPM 3 and CVPM 4”. My hope was that this would give them more time to mull over what might be a good contribution, and the results have been mixed. But read the first response to the vectors section – it’s exquisite!!

CVPM 4: Vectors: Values That Have Direction

• There is no one direction for positive or negative. The direction of the positive and the negative numbers are defined by the direction you determine. This is because if we had a normal horizontal, left to right number line the direction of negative would be left and the direction of positive would be right. However, if we were to change the way in which the number line was orientated then this would no longer apply, for example, if we made the number line move vertically the direction for negative would be down.

• If there is any displacemnent at all, then there is movement…so when you are thinking about a negative displacment dont think of it as negative movement because there still is movement

• Be careful when graphing positive and negative displacment, because they go in different directions

• You can decide if something is positive or negative only if the directions are determined for you (either by someone else or yourself).

CVPM 3: Displacement

• displacement- the change in position from the initial value to the final value

• If your initial value is negative, then in your equation it is going to be positive. ( two negatives equal a positive)

• If your initial value is negative, when you do the equation to find the displacement value, you must make it positive because you cannot subtract a negative value.

• If your initial is greater than your final and your initial is a negative, then the outcome of the equation will be positve.

• Displacement can be positive or negitive. It all depends on which way you define positive direction and negitive direction. When you don’t have initial and final placement you can try to compare and contrast the different points to surrounding objects and items.

• Based off whether or not our “Delta X” is positive/negative, we can tell if the object moved further away or closer to the reference point.

• Positive displacement is moving towards the positive side of zero

• Negative displacement is moving towards the negative side of zero

• Displacment deals with the separation points between point A and B in which the object is moving to and from, it doesnt have anything do with its path it takes to go there

• It is important to keep in mind which direction the number line/tape measure is going in order to always know which way is positive and which way is negative. If the number line is rotated differently each time the direction it wouldn’t stay constant, for example on a negative position we assume it always goes left but it could go down, right, etc. By being aware of the direction of a number line you can determine the correct change in position or displacement instead of misinterpreting it.

• When finding the delta or displacment from an object, the X initial’s position should always be measured the same way as the X final. However, the delta or displacement will always be the same if measured from the front, middle, back, etc.

##consensus ##cvpm ##practice
CVPM_Prac1_NumberLineCalculations.pdf

Displacement Calculations and Vector Quantities

I had a flash of inspiration on the train ride home from Rutgers yesterday that I was missing a few pieces on the road to discussing velocity. Specifically, I wanted students to have some practice calculating “change in” quantities in a simple setting, so they’d bump up against issues like reversing the initial and final values. More importantly, I wanted them to come up with the idea that negative values for these quantities show direction. We haven’t used the word “vector” yet, but students have already started to guess how to describe numbers “behind the x = 0 point”.

What I used today was a very simple “displacement” practice sheet, that leads students toward a few important conclusions. First, they see that the displacement of the object is the same no matter where they choose to measure, as long as they keep that point constant. Second, they see that negative position and negative displacement are two totally different things. I’m hoping that this will make it easier for them to wrap their heads around other issues of conflating positive and negative values like velocity and acceleration. We’ll see!

The “Connect” logo on the right refers to sections in their Consensus Notebook on displacement and vectors. There’s not much printed in these sections, but we took some notes to refer back to in the future.

##consensus ##cvpm ##practice ##worksheet

Buggy Lab Post-Position

We finally got to the buggy lab today! We’ve been gearing up for this moment a bit, because I wanted to firm up an idea of position before getting into the thick of CVPM. So, we spent a couple days discussing what position means, and figuring put how we can keep track of the position of a moving object by dropping salt packets at equal time intervals. The salt packets are a method that I picked up from PUM. They’re just used as place holders, but they work nicely because they stay put but are very easy to pick up. Last class, we looked at salt packet patterns for objects speeding up and slowing down. We then drew a few “dot diagrams” (a step toward motion maps that doesn’t include arrows) and interpreted them as little salt packet bread crumbs.

I decided to do prompt buggy lab by defining a research question: “What is the effect of clock reading on position?” and defining an x = 0 point and positive direction for position. Some will consider this a bit top down, but it allows us to really get into the thick of the CVPM in that first whiteboarding. Giving students freedom to investigate a phenomenon it whatever way they choose us beautiful, but feels disingenuous whenever there are some very rigid takeaways that we’re working toward. It will be useful to discuss a clock reading vs position graph as well, but having x-t graphs all around for the first whiteboard share is invaluable, because everyone in the room with have calculated a velocity when they got their best fit line.

The buggy lab itself went very well. Some students still approached the work assuming that the distance traveled is the only relevant data there to collect, and redefined a new x = 0 reference point as the starting point of the buggy. However, because we’d discussed position extensively we could talk in a very productive way about this choice. Students who had “replaced” the reference point defined by me (when I put the tape down) with the starting point recognized this, and I could then tell them that the value they were measuring was interesting, but the position relative to this other x = 0 point was important as well. Some even wrote down both values. WIN!

##cvpm ##paradigmlab ##pum